Quantum Coherence in Networks

From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing the interference pattern on the screen in a series of experimental settings where one, the other, and both slits are open unambiguously proves quantum coherence. Here we show that this is not necessary by verifying quantum coherence in a network scenario without the need for inputs. We show that there exist probability distributions for joint outcomes of three parties in a triangular network with independent sources that cannot be replicated using classical resources. Furthermore, we generalize our results to n-party networks and show that the discrepancy between correlations in classical and quantum networks increases with the number of parties. To this end, we derive nonlinear inequalities that are satisfied by classical resources (i.e., without coherence) and find quantum states that violate them.